Modified Korteweg-de Vries equation as a system with benign ghosts

Andrei Smilga

Modified Korteweg-de Vries equation as a system with benign ghosts

Číslo: 1/2022
Periodikum: Acta Polytechnica
DOI: 10.14311/AP.2022.62.0190

Klíčová slova: benign ghosts, KdV equation, integrability

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Anotace: We consider the modified Korteweg-de Vries equation, uxxx + 6u2ux + ut = 0, and explore its dynamics in spatial direction. Higher x derivatives bring about the ghosts. We argue that these ghosts are benign, i.e., the classical dynamics of this system does not involve a blow-up. This probably means that the associated quantum problem is also well defined.